Morphometric tools developed under this grant combine techniques from geometry, computer vision, statistics, and biomathematics in powerful new strategies for analysis of data about size and shape. This fourth funding period is directed to three extensions of the established core methodology, along with continued dissemination. Aim 1. Thin-plate spline interpolant aids the scientist's eye in detecting localization of interesting shape differences. Over the present funding period the applicants reported having developed an algebraic/statistical formalization of this tactic, the method of creases. Aim 1 of the renewal is to standardize the parameterization of this feature, to provide protocols for significance tests, and to produce "a grammar of grids" for uniting multiple creases into coherent summaries of empirical deformations. Aim 2. The standard Procrustes methods for discrete point landmarks have been extended for data sets of outlines. Aim 2 of the renewal is to further extend these tools for realistic data sets that combine discrete point landmarks and curves or surfaces arbitrarily. The applicants proposed to formalize statistical spaces for such structures and extend them to anticipate the emerging resource of neural tract directional data (directions without curves). Aim 3. The best current strategies for formal statistical inferences about shape exploit permutation tests of Procrustes distance or its modifications. Under new Aim 3, the applicants proposed to combine this approach with spline-based high-pass or low-pass filters and extend it further to support studies of correlations of shape with other measurement sets, including other aspects of shape. Finally, as it has been for the past twelve years, Aim 4 is to continue bringing all these methodological developments to the attention of many different biomedical communities, by primary scientific papers, essays on methodology per se, videotapes, and software and documentation free over the Internet. The work proposed is expected to extend to the medical imaging community's most sophisticated data resources, carefully labeled images and volumes, a state-of-the-art biometric toolkit for analysis and visualization carefully tuned to the special needs of such data.